James Stirling (IPPP Durham) pdfs @ LHC James Stirling (IPPP Durham) Why are pdfs important for LHC phenomenology? What do we know about pdfs? What work still needs to be done? What more can we learn about pdfs from LHC? Workshop HP2, Zurich

pdfs at LHC high precision (SM and BSM) cross section predictions require precision pdfs: th = pdf + … improved signal and background predictions → easier to spot new physics deviations ‘standard candle’ processes (e.g. Z) to check formalism (factorisation, DGLAP, …) measure machine luminosity? learning more about pdfs from LHC measurements. e.g. high-ET jets → gluon? W+/W– → quarks? forward DY → small x? … Workshop HP2, Zurich

x1P proton x2P M momentum fractions x1 and x2 determined by mass and rapidity of X x dependence of f(x,Q2) determined by fit to data, Q2 dependence determined by DGLAP equations: DGLAP evolution Q. is NLO (or NNLO) DGLAP sufficient at small x? Are higher-orders ~ αSn logm x important? Workshop HP2, Zurich

how important is pdf precision? Example 1: σ(MH=120 GeV) @ LHC σpdf  ±3%, σptNNL0  ± 10% σptNNLL  ± 8% → σtheory  ± 9% Example 2: σ(Z0) @ LHC σpdf  ±3%, σptNNL0  ± 2% → σtheory  ± 4% Example 3: quantitative limits on New Physics depend on pdfs Catani et al, hep-ph/0306211

sensitivity of dijet cross section at LHC to large extra dimensions LED accelerate the running of αS as the compactification scale Mc is approached sensitivity attentuated by pdf uncertainties in SM prediction Ferrag (ATLAS), hep-ph/0407303 Workshop HP2, Zurich

typical data ingredients of a global pdf fit Workshop HP2, Zurich

summary of DIS data + neutrino FT DIS data Note: must impose cuts on DIS data to ensure validity of leading-twist DGLAP formalism in the global analysis, typically: Q2 > 2 - 4 GeV2 W2 = (1-x)/x Q2 > 10 - 15 GeV2 Workshop HP2, Zurich

some current issues… need a better understanding of differences between pdf sets (central values and error bands): not just ‘experimental errors’ (easier) but theoretical errors/assumptions too (harder) are apparent ‘tensions’ between data sets caused by experiment or theory? is fixed–order DGLAP adequate to describe small-x F2 , FL data from HERA? If not, what are implications for LHC phenomenology? the impact of a full NNLO pdf fit? (needs NNLO jet ) Workshop HP2, Zurich

current issues contd. impact (if any) on global fits of new Tevatron jet data, new HERA structure function data, and also HERA jet data? (via γ*g→jets) flavour structure of sea: e.g. ubar  dbar and s  sbar (NuTeV) relative behaviour of u and d at large x QED/EW effects in pdfs (via O(α) corrections to DGLAP) … Workshop HP2, Zurich

pdf uncertainties MRST, CTEQ, Alekhin, GKK, … also produce ‘pdfs with errors’ typically, 30-40 ‘error’ sets based on a ‘best fit’ set to reflect ±1 variation of all the parameters* {Ai,ai,…,αS} inherent in the fit these reflect the uncertainties on the data used in the global fit (e.g. F2  ±3% → u  ±3%) however, there are also systematic pdf uncertainties reflecting theoretical assumptions/prejudices in the way the global fit is set up and performed * e.g. Workshop HP2, Zurich

pdfs with errors…. CTEQ gluon distribution uncertainty using Hessian Method output = best fit set + 2Np error sets Hessian Matrix “best fit” parameters Workshop HP2, Zurich

high-x gluon from high ET jets data both MRST and CTEQ use Tevatron jets data to determine the gluon pdf at large x the errors on the gluon therefore reflect the measured cross section uncertainties Workshop HP2, Zurich

Djouadi & Ferrag, hep-ph/0310209 Workshop HP2, Zurich

Higgs cross section: dependence on pdfs Djouadi & Ferrag, hep-ph/0310209 Workshop HP2, Zurich

Djouadi & Ferrag, hep-ph/0310209 Workshop HP2, Zurich

why do ‘best fit’ pdfs and errors differ? different data sets in fit different subselection of data different treatment of exp. sys. errors different choice of tolerance to define   fi (MRST: Δχ2=50, CTEQ: Δχ2=100, Alekhin: Δχ2=1) factorisation/renormalisation scheme/scale Q02 parametric form Axa(1-x)b[..] etc αS treatment of heavy flavours theoretical assumptions about x→0,1 behaviour theoretical assumptions about sea flavour symmetry evolution and cross section codes (removable differences!) LHC σNLO(W) (nb) MRST2002 204 ± 4 (expt) CTEQ6 205 ± 8 (expt) Alekhin02 215 ± 6 (tot) different Δχ2 similar partons different partons Workshop HP2, Zurich

tensions within the global fit with dataset A in fit, Δχ2=1 ; with A and B in fit, Δχ2=? ‘tensions’ between data sets arise, for example, between DIS data sets (e.g. H and N data, αS, …) when jet and Drell-Yan data are combined with DIS data Workshop HP2, Zurich

CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100 Workshop HP2, Zurich

Djouadi & Ferrag, hep-ph/0310209 Workshop HP2, Zurich

xg = Axa(1–x)becx(1+Cx)d MRST: Q02 = 1 GeV2, Qcut2 = 2 GeV2 xg = Axa(1–x)b(1+Cx0.5+Dx) – Exc(1-x)d CTEQ6: Q02 = 1.69 GeV2, Qcut2 = 4 GeV2 xg = Axa(1–x)becx(1+Cx)d Workshop HP2, Zurich

Note: CTEQ gluon ‘more or less’ consistent with MRST gluon easy online comparison at HEPDATA repository: durpdg.dur.ac.uk/hepdata/pfd.html

parton luminosity functions a quick and easy way to assess the mass and collider energy dependence of production cross sections s M a b i.e. all the mass and energy dependence is contained in the X-independent parton luminosity function in [ ] useful combinations are and also useful for assessing the uncertainty on cross sections due to uncertainties in the pdfs Workshop HP2, Zurich

LHC / Tevatron LHC Tevatron Campbell, Huston, S Workshop HP2, Zurich

Workshop HP2, Zurich

Standard Candle cross sections as calibration? exptl. pdf uncertainties on W, WH cross sections at LHC (MRST2001E) could (W) or (Z) be used to calibrate other cross-sections, e.g. (WH), (ZH)? (WH) more precisely predicted because it samples quark pdfs at higher x and Q2 than (W) however, ratio shows no improvement in uncertainty, and can be worse partons in different regions of x are often anti-correlated rather than correlated, partially due to sum rules. Workshop HP2, Zurich

why NNLO? The higher we calculate in fixed-order perturbation theory, the weaker the (renormalisation and factorisation) scale dependence and the smaller the theoretical error σth on the cross section  = A αS(R)N [ 1 + C1 (R) αS(R) + C2 (R) αS(R)2 + …. ] Other advantages of NNLO: better matching of partons  hadrons reduced power corrections better description of final state kinematics (e.g. transverse momentum) The calculation of the complete set of P(2) DGLAP splitting functions by Moch, Vermaseren and Vogt (hep-ph/0403192,0404111) provides the essential tool for a consistent NNLO pQCD global pdf fit. Only significant missing ingredient is NNLO correction to high-ET jet cross section. Workshop HP2, Zurich

Anastasiou, Dixon, Melnikov, Petriello (hep-ph/0306192) problem: DY @ NNLO fit  smaller high-x sea quarks  smaller high-x gluon  tension with high-ET jet fit Anastasiou, Dixon, Melnikov, Petriello (hep-ph/0306192) Workshop HP2, Zurich

NNLO features quality of global fit slightly improved αS slightly reduced sizeable change in partons in some regions of (x,Q2) new 2006 MRST NNLO pdfs (w/errors) in preparation Workshop HP2, Zurich

small x convergence of fixed-order DGLAP at small x? saturation (i.e. non-linear 1/Q2) contributions? global fit slightly improved by inclusion of HO ln(1/x) terms (Thorne, White) longer Q2 lever arm requires small-x pdf measurement at LHC DGLAP evolution? Workshop HP2, Zurich

HERA measurement of FL now likely theories with extensions at small x, both resummations and higher twist, produce quite different predictions for FL(x,Q2) from that at NLO and NNLO similar variation expected for other gluon-sensitive quantities, e.g. at LHC HERA measurement of FL now likely Thorne

forward Z0 production in LHCb … Workshop HP2, Zurich

Workshop HP2, Zurich

low-mass Drell-Yan production in ATLAS… ! Workshop HP2, Zurich

very low-mass Drell-Yan production in ALICE (pp running at 1031 cm-2 s-1) Workshop HP2, Zurich

other pdf-related quantities… Workshop HP2, Zurich

bbZ contribution to Z production @ LHC  Careful! This is in a VFNS. In a FFNS this contribution is generated by the NNLO contribution: gg→Zbb Workshop HP2, Zurich

LHC: ratio of W– and W+ rapidity distributions x1=0.52 x2=0.000064 x1=0.006 x2=0.006 ratio close to 1 because u  u etc. (note: MRST error = ±1½%) – sensitive to large-x d/u and small x u/d ratios Q. What is the experimental precision? – Workshop HP2, Zurich

! flavour decomposition of W cross sections at hadron colliders recall that the only constraint on very small x quarks from inclusive DIS (F2ep) data is on the combination 4/9 [u+c+ubar+cbar] + 1/9 [d+s+dbar+sbar] Workshop HP2, Zurich

summary and outlook origin of differences between pdf sets (central values and error bands) is largely understood, and overall MRST vs. CTEQ differences are relatively small is fixed–order DGLAP adequate to describe small-x F2 , FL data from HERA? If not, what are implications for LHC phenomenology? Can LHC measure small x pdfs? needed for LHC start-up: full NLO and NNLO pdfs with errors (needs NNLO jet ) incorporating all available HERA and Tevatron data pdf’ers still interested in flavour structure of sea: e.g. ubar  dbar and s  sbar (NuTeV). Can LHC provide information? (e.g. s g → W c ) Workshop HP2, Zurich

extra slides

QCD factorization theorem for short-distance inclusive processes where X=W, Z, H, high-ET jets, … and  known to some fixed order in pQCD and EW in some leading logarithm approximation (LL, NLL, …) to all orders via resummation ^ full NNLO pQCD, supplemented by NNLL and electroweak corrections where appropriate, is the goal for LHC

extrapolation uncertainties theoretical insight/guess: f ~ A x as x → 0 theoretical insight/guess: f ~ ± A x–0.5 as x → 0 Workshop HP2, Zurich

pdfs from global fits fi (x,Q2)   fi (x,Q2) Formalism NLO DGLAP MSbar factorisation Q02 functional form @ Q02 sea quark (a)symmetry etc. fi (x,Q2)   fi (x,Q2) αS(MZ ) Data DIS (SLAC, BCDMS, NMC, E665, CCFR, H1, ZEUS, … ) Drell-Yan (E605, E772, E866, …) High ET jets (CDF, D0) W rapidity asymmetry (CDF) N dimuon (CCFR, NuTeV) etc. Who? Alekhin, CTEQ, MRST, GGK, Botje, H1, ZEUS, GRV, BFP, … http://durpdg.dur.ac.uk/hepdata/pdf.html Workshop HP2, Zurich

uncertainty in gluon distribution (CTEQ) CTEQ6.1E: 1 + 40 error sets MRST2001E: 1 + 30 error sets Workshop HP2, Zurich

future hadron colliders: energy vs luminosity? recall parton-parton luminosity: so that with  = MX2/s for MX > O(1 TeV), energy  3 is better than luminosity  10 (everything else assumed equal!) Workshop HP2, Zurich

what limits the precision of the predictions? the order of the perturbative expansion the uncertainty in the input parton distribution functions example: σ(Z) @ LHC σpdf  ±3%, σpt  ± 2% → σtheory  ± 4% whereas for gg→H : σpdf << σpt 2% total error (MRST 2002) 4% total error (MRST 2002) Workshop HP2, Zurich

longer Q2 extrapolation smaller x Workshop HP2, Zurich

differences between the MRST and Alekhin u and d sea quarks near the starting scale ubar=dbar Workshop HP2, Zurich

Workshop HP2, Zurich

σ(W) and σ(Z) : precision predictions and measurements at the LHC σNLO(W) (nb) MRST2002 204 ± 4 (expt) CTEQ6 205 ± 8 (expt) Alekhin02 215 ± 6 (tot) different Δχ2 similar partons different partons 4% total error (MRST 2002) Workshop HP2, Zurich

±2% ±3% contours correspond to ‘ experimental’ pdf errors only; shift of prediction using CTEQ6 pdfs shows effect of ‘theoretical’ pdf errors Workshop HP2, Zurich

Workshop HP2, Zurich

Workshop HP2, Zurich

Workshop HP2, Zurich

(LO) W cross sections at the Tevatron and LHC using (NLO) partons from MRST, CTEQ and Alekhin B.σ(W) (nb) MRST2002 2.14 CTEQ6 2.10 Alekhin02 2.22 LHC B.σ(W+) (nb) B.σ(W) (nb) W+/W– MRST2002 10.1 7.6 1.33 CTEQ6 10.2 1.34 Alekhin02 10.7 7.9 1.35 1 1.06783675 1.06783675 2.1356735 1. 2 1.11121871 1.11121871 2.22243741 1. 3 1.05158736 1.05158736 2.10317472 1. 1 10.1224375 7.6098974 17.7323349 1.33016741 2 10.6896677 7.91142539 18.6010931 1.35116836 3 10.1753947 7.59305006 17.7684447 1.34009319 Workshop HP2, Zurich

differences between the MRST, CTEQ and Alekhin strange quarks near the starting scale Workshop HP2, Zurich

effect of NNLO correction on Higgs production at LHC Workshop HP2, Zurich